Computing the regression to the mean effect?
The below example uses equation (1) of Barnett, AG, van der Pols1, JC and Dobson, AJ (2005) 34 215-220 which uses the example below where only people with a score of 40 or below were sampled at baseline from a population with a mean of 60 and a standard deviation of 15.
* Taken from http://hisdu.sph.uq.edu.au/lsu/adrian/rtmcode.htm#Rcode # Change these parameters depending on your data; sigma<-15; # total std; mu<-60; # population mean; cut<-40; # cut-off; # Loops to run through rho and m scenarios; sigma2_w=vector(length=11,mode="numeric") sigma2_b=vector(length=11,mode="numeric") Rl=vector(length=11,mode="numeric") Rg=vector(length=11,mode="numeric") rho=vector(length=11,mode="numeric") for (rhox in 0:10){ rho[rhox+1]<-rhox/10 sigma2_w[rhox+1]<-(1-rho[rhox+1])*(sigma^2); # within-subject variance; sigma2_b[rhox+1]<-rho[rhox+1]*(sigma^2); # between-subject variance; for (m in 1:1){ # Number of baseline measurements; zg<-(cut-mu)/sigma; # z; zl<-(mu-cut)/sigma; # z; x1g<-dnorm(x=zg); # phi - probability density; x2g<-1-pnorm(q=zg); # Phi - CDF x1l<-dnorm(x=zl); # phi; x2l<-1-pnorm(q=zl); # Phi; czl<-x1l/x2l; # C(z) in paper; czg<-x1g/x2g; # C(z) in paper; Rl[rhox+1]<-(sigma2_w[rhox+1]/m)/sqrt(sigma2_b[rhox+1]+(sigma2_w[rhox+1]/m))*czl; # RTM effect, Equations (1) m=1 & (2) m>1; Rg[rhox+1]<-(sigma2_w[rhox+1]/m)/sqrt(sigma2_b[rhox+1]+(sigma2_w[rhox+1]/m))*czg; # RTM effect; } } output<-cbind(sigma2_b,sigma2_w,rho,Rl,Rg) print("The expected RTM effect for a range of baseline samples sizes and rhos") print(output) print("sigma2_b=between-subject variance, sigma2_w=within-subject variance") print("rho=within-subject correlation, Rl=RTM effect (<cut-off), Rg=RTM effect (>cut-off)");